use the distributive property to rewrite the polynomial (2x+1)(x-4)

Answer 1

To use the distributive property to rewrite the polynomial $(2x+1)(x-4)$, we will distribute each term in the first polynomial by each term in the second polynomial.

1. Distributing $2x$ to both terms in $(x-4)$: $$2x\cdot x=2x^2$$ $$2x\cdot (-4)=-8x$$

2. Distributing $1$ to both terms in $(x-4)$: $$1\cdot x=x$$ $$1\cdot (-4)=-4$$

Now combine all the results: $$2x^2-8x+x-4$$

Next, combine like terms $-8x+x$: $$2x^2-7x-4$$

So, the polynomial $(2x+1)(x-4)$ rewritten is: $$\boxed{{\displaystyle 2x^2-7x-4}}$$

Answer 2

2 is right but the other ones are not

Answer 3

Let's redo the calculation for $(2x+1)(x-4)$ using the distributive property step by step.

1. Distribute $2x$ over $(x-4)$:

   • $2x\cdot x=2x^2$
   • $2x\cdot (-4)=-8x$

2. Distribute $1$ over $(x-4)$:

   • $1\cdot x=x$
   • $1\cdot (-4)=-4$

Now, we combine all these terms: $$2x^2-8x+x-4$$

Next, combine the like terms $-8x+x$: $$2x^2-7x-4$$

The final rewritten polynomial is: $$\boxed{{\displaystyle 2x^2-7x-4}}$$

Please let me know if there's something specific you believe is incorrect or if there's further clarification needed!